Minimax design of FIR Nyquist filters using a quadratic programming method

FIR Nyquist filters play important roles in communication applications. Minimax filters are very attractive because of their minimal maximum approximation error. Minimax FIR Nyquist filters, however, may not satisfy the alternating theorem. Thus the efficient multiple-exchange design algorithms are not guaranteed to converge or may not converge to minimax filters. By trading off the minimax and the least-squares criterions, a positive definite quadratic programming formulation of the design problem is obtained. It is shown that under sufficiently small tradeoff factor, the resulted filter is actually a minimax one. Using this method, many FIR Nyquist filters have been designed. Comparison with existing algorithms demonstrates the effectiveness and the efficiency of the method.